You should have told them you couldn't do it as soon as they told you. Worst case is they reject you, best case is they make accommodations for you, either way it's better to be honest than to try and hide it.

I'd also suggest that any employer who makes you want to travel two hours each way for training (for what I assume is a low level role, it would be different if it were paid well) is probably not an employer you want to work for.

........and you didn't think you might need to somehow make a travel arrangement beforehand? Both before any interviews, and if hired? Even if it was within walking or biking distance, in inclement weather, you really don't want to take a risk being exposed like that. Sorry, YDI.